In case this helps someone, I'm posting a direct answer.

SpanContext spanContext =
  SpanContext.create(
    IdGenerator.random().generateTraceId(),
    IdGenerator.random().generateSpanId(),
    TraceFlags.getDefault(),
    TraceState.getDefault());


...

logRecordBuilder.setContext(Context.current().with(Span.wrap(spanContext)));
logRecordBuilder.emit();
...

https://github.com/open-telemetry/opentelemetry-java-instrumentation